function [tp, fp] = roc(t, y)
%
% ROC - generate a receiver operating characteristic curve
%
% [TP,FP] = ROC(T,Y) gives the true-positive rate (TP) and false positive
% rate (FP), where Y is a column vector giving the score assigned to each
% pattern and T indicates the true class (a value above zero represents
% the positive class and anything else represents the negative class). To
% plot the ROC curve,
%
% PLOT(FP,TP);
% XLABEL('FALSE POSITIVE RATE');
% YLABEL('TRUE POSITIVE RATE');
% TITLE('RECEIVER OPERATING CHARACTERISTIC (ROC)');
%
% See [1] for further information.
%
% [1] Fawcett, T., "ROC graphs : Notes and practical
% considerations for researchers", Technical report, HP
% Laboratories, MS 1143, 1501 Page Mill Road, Palo Alto
% CA 94304, USA, April 2004.
%
% See also : ROCCH, AUROC
%
% File : roc.m
%
% Date : Friday 9th June 2005
%
% Author : Dr Gavin C. Cawley
%
% Description : Generate an ROC curve for a two-class classifier.
%
% References : [1] Fawcett, T., "ROC graphs : Notes and practical
% considerations for researchers", Technical report, HP
% Laboratories, MS 1143, 1501 Page Mill Road, Palo Alto
% CA 94304, USA, April 2004.
%
% History : 10/11/2004 - v1.00
% 09/06/2005 - v1.10 - minor recoding
% 05/09/2008 - v2.00 - re-write using algorithm from [1]
%
% Copyright : (c) G. C. Cawley, September 2008.
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
%
ntp = size(y,1);
% sort by classeifier output
[y,idx] = sort(y, 'descend');
t = t(idx) > 0;
% generate ROC
P = sum(t);
N = ntp - P;
fp = zeros(ntp+2,1);
tp = zeros(ntp+2,1);
FP = 0;
TP = 0;
n = 1;
yprev = -realmax;
for i=1:ntp
if y(i) ~= yprev
tp(n) = TP/P;
fp(n) = FP/N;
yprev = y(i);
n = n + 1;
end
if t(i) == 1
TP = TP + 1;
else
FP = FP + 1;
end
end
tp(n) = 1;
fp(n) = 1;
fp = fp(1:n);
tp = tp(1:n);
% bye bye...